Implied Volatility Research Articles

Volatility and the Cross-Section of Returns on FX Options

We study the cross-section of returns on FX options sorting currencies based on implied volatilities (IV). Long straddle positions in currencies with low (high) implied volatilities perform well (poorly). A long low IV-short high IV strategy produces large average returns after transactions costs. Total volatility matters rather than any component or transformation of volatility. The returns are distinct from those in the literature on foreign exchange returns or equity option returns and cannot be explained convincingly by standard risk factors. We argue mispricing is caused by cross-sectional differences in hedging demand combined with limits to arbitrage.

Commodity Option Implied Volatilities and the Expected Futures Returns

The detrended implied volatility of commodity options (VOL) forecasts the cross section of the commodity futures returns significantly. A zero-cost strategy that is long in low VOL and short in high VOL commodities yields an annualized return of 12.66% and a Sharpe ratio of 0.69. Notably, the excess returns based on the volatility strategy emanate mainly from its forecasting power for the future spot component, different from the other commodity strategies examined so far in the literature which are all driven by roll returns. This strategy demonstrates low correlations (below 10%) with the other strategies such as momentum or basis and performs especially well in recessions. Our results are robust after controlling for illiquidity, other commodity pricing factors, and exposure to the aggregate commodity market volatility. The VOL measure is associated with hedging pressure on the futures and especially on the options market. News media also helps amplify the uncertainty impact. Variables related to investors’ lottery preferences and market frictions are able to explain part of the predictive relationship.

Tighter Bounds for Implied Volatility

In this note, we establish bounds on Black-Scholes implied volatility that substantially improve on the uniform bounds previously derived by Tehranchi for most options likely to be encountered in practical applications.

Implied volatility and skewness surface

The Homoscedastic Gamma (HG) model characterizes the distribution of returns by its mean, variance and an independent skewness parameter. The HG model preserves the parsimony and the closed form of the Black–Scholes–Merton (BSM) while introducing the implied volatility (IV) and skewness surface. Varying the skewness parameter of the HG model can restore the symmetry of IV curves. Practitioner’s variants of the HG model improve pricing (in-sample and out-of-sample) and hedging performances relative to practitioners’ BSM models, with as many or less parameters. The pattern of improvements in Delta-Hedged gains across strike prices accord with predictions from the HG model. These results imply that expanding around the Gaussian density does not offer sufficient flexibility to match the skewness implicit in options. Consistent with the model, we also find that conditioning on implied skewness increases the predictive power of the volatility spread for excess returns.

Common Functional Principal Components

Functional principal component analysis (FPCA) based on the Karhunen-Loeve decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal components for two sample problems. Our research is motivated not only by the theoretical challenge of this data situation but also by the actual question of dynamics of implied volatility (IV) functions. For different maturities the logreturns of IVs are samples of (smooth) random functions and the methods proposed here study the similarities of their stochastic behavior. Firstly we present a new method for estimation of functional principal components from discrete noisy data. Next we present the two sample inference for FPCA and develop two sample theory. We propose bootstrap tests for testing the equality of eigenvalues, eigenfunctions, and mean functions of two functional samples, illustrate the test-properties by simulation study and apply the method to the IV analysis.

Implied Volatility and Predictability of GARCH Models

We have examined the predictive power of GARCH model to forecast return volatility for Nifty 50 index. Realized volatility, which is the sum of intraday squared returns, is used as the proxy for the true volatility. Three models of the GARCH family have been used to forecast return volatility i.e., GARCH, GJR-GARCH and EGARCH along with their implied volatility (IV) augmented counterparts i.e., GARCH IV, GJR-GARCH IV and EGARCH IV. Implied Volatility forecasting has been done using AR, MA, ARMA, ARIMA and Random Walk. But GARCH model augmented with implied volatility performs better than GARCH models without augmentation or implied volatility alone. Forecasting performance of the competing models has been judged by using mean absolute error (MAE) and root mean squared error (RMSE). MAE and RMSE show that GARCH IV model is best suited for the volatility forecasting in the context of Nifty 50 index.

US Implied Volatility as A predictor of International Returns

This study provides evidence of the US implied volatility’s e ect on international equitymarkets’ returns. This evidence has two main implications: i) investors may find that foreign equityreturns adjusting to US implied volatility may not provide true diversification benefits, and ii) foreignequity returns may be predicted using US implied volatility. Our sample includes US volatility index(VIX) and major equity indexes in twenty countries for the period between January, 2000 throughJuly, 2017. VIX leads eighteen of the international markets and Granger causes seventeen of themarkets after controlling for the S&P-500 index returns and the 2007/2008 US financial crisis. USinvestors looking to diversify US risk may find that international equities may not provide intendeddiversification benefits. Our evidence provides support for predictability of international equity returnsbased on US volatility.

Treasury Yield Implied Volatility and Real Activity

We show that at-the-money implied volatility of options on futures of 5-year Treasury notes (Treasury ‘yield implied volatility’) predicts both the growth rate and volatility of gross domestic product, as well as of other macroeconomic variables, like industrial production, consumption, and employment. This predictability is robust to controlling for the term spread, credit spread, stock returns, stock market implied volatility, and several other variables that prior literature showed to predict macroeconomic activity. Our results indicate that Treasury yield implied volatility is a useful forward-looking state variable to characterize risks and opportunities in the macro economy.

A Forecast Comparison of GARCH Models and Implied Volatility

This research paper empirically investigates the performance of various models of volatility forecasting. Along with “unconditional standard deviation”, most commonly use measure of volatility, present research considered six others models of volatility forecasting, namely Standard GARCH (Generalized Autoregressive Conditional Heteroscedasticity) model, GJR-GARCH model, Exponential GARCH model (eGARCH), Asymmetric Power GARCH model (apGARCH), Component Standard GARCH model (csGARCH), and Option Implied Volatility model. To forecast volatility, the daily closing values of NSE Nifty 50 (Index) are considered from period 1st April 2002 to 31st March 2015, a span of 13 years. The present study found no single model as the best performing model. Overall performance found GJR-GARCH and option implied volatility having consistence performance. Interestingly, most commonly used model i.e. unconditional standard deviation found to be the worst model among all models studies in present research.

Linkage between India Implied Volatility Index and Stock Index Returns

The present study examines the linkage between the change in implied volatility index and the underlying stock index return in the Indian stock market. The empirical results revealed that the contemporaneous return is the most important factor that determines the changes in the current India implied volatility. Besides, the empirical evidences confirm the negative asymmetry volatility-return relation, supporting the behavioral explanations (the affect and representativeness heuristics) rather than financial leverage hypothesis.

Option Prices Incorporate Fundamentals: Evidence from US Natural Gas Market

We examine the incremental power of a large set of key fundamental, financial, and macroeconomic variables for forecasting the volatility of natural gas futures prices. Among other results, we find that the option implied volatility (IV) significantly improves the performance of predictions regarding the future volatility of the natural gas market. We also identify several fundamental and macroeconomic variables (e.g., open interests, default premiums, and the return of the housing index) which are statistically-significant in a predictive regression even after including the option implied volatility. On the other hand, we do not find a substantial increase in the adjusted-R2 of the predictive regressions (including IVs) after adding significant fundamental variables. The small incremental predictive power of fundamental variables is interpreted as a sign of the efficiency of the options market. We also observe that the adjusted-R2s of predictive regressions are higher when the time-to-maturity of the futures contract increases. Our results can help users of natural gas volatility forecasts (e.g., producers, utility companies, and portfolio managers) make better informed and more efficient operational and financial decisions.

Behaviour and determinants of implied volatility in Indian market

Purpose The purpose of this paper is to understand the patterns of the implied volatility (IV) of the Indian index option market and its relationship with moneyness (called the volatility smile). Its goal is also to ascertain the determinants of IV. Design/methodology/approach For this purpose, IVs were computed from the daily call and put data of CNX Nifty index options from April 2004 to March 2014. The patterns of IVs were analysed using univariate parametric tests. Multivariate regression analyses were conducted to understand the relationships observed. Resultantly, vector autoregressions were performed to assess the determinants of IV. Findings The results suggested that there was asymmetric volatility across time and strike prices using alternative measures of moneyness. Furthermore, it was found that the IV of lower strike prices was significantly higher (lower) than that of higher strike prices for call (put) options. Put IV was observed to be higher than call IV irrespective of any attributes. The results further showed that current-month contracts have significantly higher IV than those for next month and those were followed by far-month contracts. Nifty futures’ volumes and momentum were found to be significant determinants of IV. Practical implications The behaviour of the volatility smile is important when accounting for the Vega risks in the portfolios of hedge fund managers. While taking a position, besides the Black-Scholes-Merton (BSM) model’s input factors, investors must consider the previous behaviour of volatility, a market’s microstructures and its liquidity for a put option contract. They must also consider the attributes of the underlying for a call option contract. Originality/value This is the first decadal study (the longest span of data for any international study on this subject) to confirm the existence of the volatility smile for the index options market in India. It examines and confirms the smile’s asymmetry patterns for different definitions of moneyness, as well as option types, the tenure of options contracts and the different phases of market conditions. It further helps to identify the determinants of IV and so has renewed importance for traders.

Volatility Forecast Using GARCH, News Sentiment and Implied Volatility

Due to its significance, forecasting asset volatility has been an active area of research in recent decades. In this whitepaper we aim to take into account the stylised facts of volatility to improve predictive power of a simple GARCH model. We investigate the power of three GARCH models (GARCH, EGARCH, GJR- GARCH) using implied volatility and news sentiment data as external regressors in order to enhance forecasts of stock return volatility. We also explore the impact of the use of fat-tailed and skewed distributions. Analysis is conducted on 5 constituents of the S&P500. In terms of in-sample performance, the findings suggest that a GJR-GARCH(1,1) model incorporating a student-t distribution, implied volatility and news sentiment data consistently out-performs a simple GARCH(1,1) with a normal distribution. When comparing out-of-sample forecast performance, the enhanced models were able to improve volatility predictions for four out of five stocks.

Option-Implied Volatility Measures and Stock Return Predictability

Do changes in implied volatilities (IVs) or differences among options at different spots on the volatility surface contain predictive information for future returns? The question has been asked repeatedly—and often answered in the affirmative for specific measures—but questions remain. In this article, the authors perform a comparison test on six return predictors that are all computed as differences among implied and realized volatilities and that have been proposed in the literature. The authors consider more measures, more maturities, and longer samples than earlier articles, and they include a variety of appropriate control variables. They find that the difference between at-the-money (ATM) call and put IV (CPIV) and out-of-the-money (OTM) put IV minus ATM call IV are both highly significant at the individual stock level, while a long–short portfolio strategy based on realized minus implied volatility does very well. The alternative volatility combinations are substantially less effective as return predictors.

Forward at the Money Forward Implied Volatility and Forward Underlying Move Estimations

Ahead of the 23rd June UK referendum on Brexit, this note provides a technique for estimating the Forward (at referendum date) At The Money Forward (ATMF) implied volatility for equity or FX Indexes. We provide a closed form formula for the forward underlying expected moves (for short terms maturities) post the referendum date. We provide a closed form formula for the forward underlying expected moves conditional to the adverse event (vote in favour of 'leaving' the European Union (EU) area) happening. We finally provide a closed form formula for the forward underlying expected moves conditional to the adverse event not happening. More generally the framework here can be used to estimate forward implied volatility and forward asset price moves post a potentially adverse event to come in the future.

Relationship of the Change in Implied Volatility with the Underlying Equity Index Return in Thailand

The main purpose of this study is to examine the relationship between the change in implied volatility index and the underlying stock index return. The dataset used in this study is from 11/19/2010 to 12/27/2013. The regression analysis is performed on stationary series. The empirical results reveal that there is evidence of a significantly negative and asymmetric relationship between the return and the change in implied volatility in the Thai stock market. The finding in this study gives implication for risk management.

Los productos financieros derivados y la política monetaria: evidencia para la Reserva Federal (2000-2015)

While the use of money market derivative products was increasing, many research studies were published on how derivative products affect the implementation of monetary policies. In the theoretical framework of an interest rate forecasting model (Taylor rules), we will use the generalised method of moments (GMM) to compare the influence of financial derivative products over the Federal monetary policy carried out from the year 2000 to 2015. By means of this analysis we may conclude that the implicit volatility of the derivatives markets is an explanatory variable of the behaviour of the short-term nominal interest rate.

Stein’s Overreaction Puzzle: Option Anomaly or Perfectly Rational Behavior?

Among the many anomalies researchers have uncovered in financial markets is Stein’s finding that implied volatilities (IVs) from long-term options are too sensitive to short-shortrun volatility shocks. Option investors overreact to a spike in implied volatility for nearby contracts, and volatilities rise across the maturity spectrum, in contradiction to the smoothing effect when a mean-reverting time series is averaged over a long period. Lehnert, Lin, and Martelin have found a plausible explanation in the fact that mean-reversion of volatility estimated from stock returns is an empirical estimate, while implied volatilities are risk-neutralized values. They show that risk-neutral mean reversion is much slower than in the empirical process. Moreover, it depends on investors’ risk aversion, so that the “overreaction” effect caused by sluggish reversion toward long-run average volatility should be greatest when investors are most averse to risk. They then demonstrate that the theoretical argument is supported by the data. Long-maturity options show significant overreaction to short-maturity IV changes, but the effect is much stronger during periods of market upset. The options market appears to be more rational than Stein’s results suggest.

A New Factor to Explain Implied Volatility Smirk

In this paper we find empirical evidence of a new smirk factor, obtained from the jump structure of the risk neutral distribution of the underlying Levy process. As an application we show how to price a barrier style contract.

Implied Volatility of the KOSPI 200 Index Option Market

This paper analyzes implied volatilities (IVs), which are computed from trading records of the KOSPI 200 index option market from January 2005 to December 2014, to examine major characteristics of the market pricing behavior. The data includes only daily closing prices of option transactions for which the daily trading volume is larger than 300 contracts. The IV is computed using the Black-Scholes option pricing model. The empirical findings are as follows; Firstly, daily averages of IVs have shown very similar behavior to historical volatilities computed from 60-day returns of the KOSPI 200 index. The correlation coefficient of IV of the ATM call options to historical volatility is 0.8679 and that of the ATM put options is 0.8479. Secondly, when moneyness, which is measured by the ratio of the strike price to the spot price, is very large or very small, IVs of call and put options decrease days to maturity gets longer. This is partial evidence of the jump risk inherent in the stochastic process of the spot price. Thirdly, the moneyness pattern showed heavily skewed shapes of volatility smiles, which was more apparent during the global financial crises period from 2007 to 2009. Behavioral reasons can explain the volatility smiles. When the moneyness is very small, the deep OTM puts are priced relatively higher due to investors’ crash phobia and the deep ITM calls are valued higher due to investors’ overconfidence and confirmation biases. When the moneyness is very large, the deep OTM calls are priced higher due to investors’ hike expectation and the deep ITM puts are valued higher due to overconfidence and confirmation biases. Fourthly, for almost all moneyness classes and for all sub-periods, the IVs of puts are larger than the IVs of calls. Also, the differences of IVs of deep OTM put ranges minus IVs of deep OTM calls, which is known to be a measure of crash phobia or hike expectation, shows consistent positive values for all sub-periods. The difference in the financial crisis period is much bigger than in other periods. This suggests that option traders had a stronger crash phobia in the financial crisis.